ADVANCED: Randomization

GVPT399F: Power, Politics, and Data

Randomization

  • Last session, we randomly assigned 1,000 hypothetical people to two different groups

  • Testing whether randomization helps us create two roughly identical groups prior to treatment

  • You now have a lot of the R code needed to replicate that analysis

Creating our group of 1,000 people

Imagine we have a group of 1,000 individuals. We know the following about them:

  • Height

  • Weight

  • Eye colour

Creating our group of 1,000 people

group_df <- tibble(
  id = 1:1000,
  height = rnorm(1000, 170, 6),
  weight = rnorm(1000, 80, 10),
  eye_colour = sample(c("Blue", "Green", "Brown", "Grey"), 
                      1000, 
                      replace = T)
)

group_df
# A tibble: 1,000 × 4
      id height weight eye_colour
   <int>  <dbl>  <dbl> <chr>     
 1     1   167.   87.7 Grey      
 2     2   174.   88.9 Brown     
 3     3   166.   67.3 Blue      
 4     4   167.   75.0 Blue      
 5     5   171.   79.3 Green     
 6     6   171.   93.4 Blue      
 7     7   169.   73.0 Blue      
 8     8   171.   97.0 Brown     
 9     9   168.  101.  Grey      
10    10   177.   63.7 Green     
# ℹ 990 more rows

The Normal distribution

ggplot() + 
  geom_density(aes(x = rnorm(n = 1e6, mean = 0, sd = 1))) + 
  theme_minimal()

Random sampling from the Normal distribution

I can take a random sample of n values from a Normal distribution centered at some mean with a specific standard deviation.

  • By default, rnorm() takes a mean of 0 and a standard deviation of 1

  • The following code takes 1,000 random samples from that default Normal distribution

Random sampling from the Normal distribution

rnorm(n = 1000, mean = 0, sd = 1)
   [1]  0.292020319 -0.409000913 -0.321004413  0.421836147 -0.464534082
   [6]  2.147159680  0.983973736  0.604063988  0.084842380 -1.044421676
  [11] -1.088959905 -0.970797957  0.339034110 -0.152853450 -0.767582773
  [16]  1.808857225  0.011690560  0.146620563 -0.163913988 -3.565672566
  [21] -0.720706842  0.243213973 -0.580144958  1.430459297 -2.121926784
  [26]  0.422833321  1.128105146 -0.485566752  1.234329655  1.698482667
  [31] -0.668351524  0.949503313 -0.493915280 -1.549429666 -0.145453144
  [36] -1.549819412 -0.129683467 -2.716803538  0.670184618  0.188682734
  [41] -1.203307388  1.449606357  0.221445849 -0.012063904  0.268946364
  [46]  0.827707532 -0.706101399  0.414462599 -1.319816413  0.941550572
  [51] -0.883147943  0.985152524  1.103401988 -0.269698585 -0.171960595
  [56] -0.674203609 -0.859620142  0.560260225 -0.119747335 -0.550844091
  [61]  1.283947650 -0.644179263  0.852721136 -1.388056277  0.806883122
  [66] -0.238484695  0.111927858  1.030094858  0.735603876  0.337953859
  [71] -0.905346147 -1.591674535  0.463970260  1.863302622  0.884069853
  [76]  0.086932745  0.170688658  1.966468863  0.983008410 -0.001938640
  [81]  0.326917060 -0.108082428 -0.834533583 -1.054803133  0.431685505
  [86] -2.149163658 -0.929332440  0.488873479  0.292699585 -0.939171940
  [91] -0.388673436 -1.109346108 -0.189608579  1.011821653  1.142893868
  [96] -0.173188563 -0.497755885  1.139869668  0.298790682 -0.524798136
 [101]  0.856562232  0.008562427  0.273124095 -1.687594865  0.415600399
 [106]  0.469447269  0.256272447  1.621481103 -1.183566584  1.356741705
 [111] -0.706616950  0.900887929  1.144463784  0.744513644  0.285408354
 [116]  1.005575264 -0.671940691  0.594348687  0.719381831  0.653745867
 [121] -1.524117253  0.825624488 -0.896210721  0.841299679 -1.546667570
 [126] -0.660569219  1.489055787  0.117615265 -1.651488783 -2.287292326
 [131]  0.960055406  0.732473754 -0.782483524  0.573367761  1.586253342
 [136] -1.396725846 -1.289890429 -2.715807437 -0.287527832  0.633939691
 [141] -0.950455095  1.738394175  0.349090293 -0.690784301  0.270004240
 [146]  1.251280381 -1.204117634  0.418146080 -0.853615219 -1.000288741
 [151] -0.482747369  0.498034221  1.026472014 -0.394065064 -0.542146683
 [156] -2.393360992  0.207167143 -0.772571566 -1.656891882 -0.044635733
 [161] -1.514540772  0.987295320 -0.036996455 -2.026206546  0.002965054
 [166]  0.403255185 -0.517822916 -1.050989078 -0.080328577 -1.491044929
 [171]  0.759336139  0.308164244  1.717672849 -2.160752877 -0.771015665
 [176] -0.510747856 -2.334937255  0.524920537 -0.097729819 -0.410001318
 [181] -0.327913967 -1.406769188 -0.812130302 -1.686113370 -0.035678244
 [186]  0.487045171  1.666290310  0.001830093 -1.139846941  0.471583627
 [191] -1.810398458 -1.006429498 -0.428006879  2.367183746 -0.757372147
 [196] -2.078946168  0.461596365 -0.112909939 -0.351260858  1.368535929
 [201] -0.460948030 -0.329054289  0.370911054 -0.259973382  0.772874318
 [206] -0.571584864 -1.389701632  1.058872200  2.533121474 -0.138826387
 [211]  1.648946300  0.276213561  2.112143068 -0.636252038  1.508707860
 [216]  1.406213289  0.293420989  1.430383560 -2.110375755 -1.780701320
 [221]  1.983735091  0.367626308  0.093397403 -0.760740590 -0.654282524
 [226]  0.671167766 -0.914129677 -0.155518095  0.648266874  0.072552099
 [231]  0.518048205  0.989548843 -0.205660235  0.763317884 -0.915921926
 [236] -0.359374088  0.049288503 -0.580774338  0.316127566  1.044498734
 [241]  1.046581984  1.111248512 -0.897070974 -0.256357886 -1.066338597
 [246]  0.594369190 -0.173793424  0.701243940 -1.189347076 -1.238004827
 [251]  0.286827538 -1.253096568  2.824196679  1.327841250 -0.268778319
 [256]  0.606589212  0.226017119 -0.264163659 -0.035942481 -0.958470957
 [261]  0.561532788 -0.487812723 -0.391901698 -0.399592539  0.352660551
 [266] -0.526679565 -0.739491932 -2.673339017  2.302494274  1.205349603
 [271]  0.783210968 -2.162518224 -0.546096275 -0.901812939  1.389570842
 [276] -0.824384390  2.124165274  0.877056407  0.486288226  1.523315306
 [281]  0.729699453  0.029869319  1.501277825  0.814793499 -0.143391097
 [286]  0.844362158  0.242104572 -0.082557621 -0.167543053 -0.542912905
 [291]  0.303040629  0.013395309  0.859669421 -0.786696826 -0.664593529
 [296]  0.773738475  0.617979114  1.644178531  0.447842069 -1.675331033
 [301] -0.746840809  0.498461591 -0.152589348 -1.419038664 -0.088359813
 [306]  0.393136144  0.876251658 -0.640025768 -0.100226187  0.037254596
 [311]  0.463314640  0.045902435  0.744808287  1.086615862 -1.072028253
 [316] -1.450977011 -0.611514715  0.385455677  1.234791011 -0.858049283
 [321]  0.269617276  0.738962758 -1.901948588  1.737413557  0.874308387
 [326] -1.621152195 -0.888153041  1.340962317  0.244048653 -0.416637112
 [331]  0.924286379  1.204793437 -1.173728777  0.523178990  1.181227342
 [336] -1.479813829 -1.956957211 -0.090607356  0.627840712  0.073019281
 [341] -1.182438945  0.383475882 -0.761309581  2.060380594  1.521846427
 [346]  1.564257165  0.427263173  0.547372654 -0.505484347 -1.412887488
 [351] -0.054472726  1.615740385 -0.360302981 -0.698441803  0.111895149
 [356] -0.233077138  0.716892938 -0.563731693  1.437618634  1.823293068
 [361]  0.722394344  1.243648060  2.131943834  0.402213553  0.844499687
 [366]  0.006823726  0.757656407  0.533857501  1.469967891 -0.795763528
 [371]  0.638388330  2.346589281 -1.076978706  0.222765089  2.270134008
 [376]  0.696616075 -2.106570614 -0.316026529  0.938559806 -1.620947423
 [381] -0.284759320  0.978048256  0.702736366  1.486762554 -0.144383261
 [386] -0.362221454 -0.290609096 -0.123124613  1.134172182 -0.146876811
 [391] -0.671836041 -0.543577017  0.009621964 -1.302381403  0.937347882
 [396] -0.284488314 -0.710582001  1.592729871  1.138712787  0.006748575
 [401]  2.633817212 -0.312776762  0.870705701 -0.515173123 -1.024850294
 [406] -0.289655742  0.824398008 -0.365106551  1.665784730 -0.266280932
 [411]  0.240587603 -0.854617095  0.128122706 -1.275229205  1.376164110
 [416]  1.265617737  0.597594401  1.124082778  3.053340036 -1.023403829
 [421]  2.347345457 -0.356676251  0.217141163 -0.784478948  0.953067057
 [426] -0.879936400 -1.785929546 -1.359333079  0.401962010 -1.235738332
 [431]  0.806005501 -1.448821817  1.547414915  0.925792989 -0.688067194
 [436] -1.006213783 -0.836685796  1.363100003 -0.086615377  1.080842991
 [441]  0.697381337  0.992561500 -0.346911583  1.745687516  1.277061725
 [446]  0.346677199 -0.513447573 -0.587328499  0.036667282 -0.539611616
 [451]  0.134940899  0.745207543 -0.343795269  0.815385315  1.715233997
 [456]  0.137893670 -0.179362352 -0.472750838 -0.010623699  0.558944015
 [461]  0.345941044 -0.894967277 -0.526518709 -0.338172937 -1.621969195
 [466]  1.695943778 -0.208556487 -1.149758051 -0.045918883 -0.234214508
 [471] -0.487171700 -0.082450386 -0.571034591 -1.081031610 -0.751880878
 [476] -0.798425607  0.813942474  1.500723421  0.203016769  0.714242463
 [481]  0.557463873  1.438241241  1.615390106 -1.500586299  0.141547766
 [486] -1.260000071  1.157989767  0.004057867 -0.887303709  0.251777253
 [491]  0.257533789 -0.757088878 -0.316876971  0.187847721  0.399432308
 [496] -1.021656329  1.531144215 -1.763224631 -0.248106801  1.627194918
 [501] -0.396163231  2.229665798  0.076892431  0.409334135  1.517728038
 [506] -3.050542030  0.615811240 -0.119846103  1.161892806 -0.716989365
 [511] -0.052440132 -1.245022000  1.501193219  0.833601332  0.400994458
 [516]  0.723935373  0.804876004  1.036839673  0.146014402  0.227791125
 [521]  1.682163177  1.666964160  1.319394605  0.315528273 -1.713764211
 [526] -0.139719394  0.267071195  0.793338239 -1.259636559 -1.523288657
 [531] -0.483262232  1.594253547  2.014846335  0.116545190 -0.865448571
 [536] -0.643039206  0.043117115  1.274586440 -0.776749270 -0.331859587
 [541] -1.594833727  0.772692729  0.360362635 -1.089440125  1.246470732
 [546]  0.820638508 -0.102591979  0.182631954 -0.509525716  0.216120372
 [551]  0.479928985 -0.754192828  0.253591396 -1.002978079 -0.718179966
 [556]  0.334546503  0.242998451  1.260100187  0.139086548  0.570155871
 [561]  0.875425442 -1.119202319 -0.993025734  1.831102358  1.346817700
 [566]  0.159300439  0.477484824  0.464679864  0.572049722 -1.406109731
 [571] -0.592977511  1.365309659 -0.622530483 -1.071072803 -1.007920464
 [576] -0.996237698  0.625568317 -0.167605305 -1.321228545 -0.852480096
 [581]  2.290157400 -1.133969761 -0.090298423  0.336857049  1.640282105
 [586]  1.550776922 -0.882230801  2.000275497  0.184913849 -0.895394255
 [591]  0.931540094  0.517132955  0.767627428 -0.544532337 -0.677123311
 [596]  0.345136695  0.201663239  0.598076136 -0.972509737 -0.415284081
 [601] -1.059013606  1.709095678 -1.354711519  0.806648121  0.975509007
 [606]  2.565665376 -0.261414478  0.932494454 -0.499659702  0.270159554
 [611] -0.047670007 -0.181014613 -0.071717365 -0.151356362  0.543424676
 [616] -1.145023179 -0.207123346 -0.643217432  0.848374102  0.314187051
 [621] -0.688548892 -0.508643592 -2.020191572 -0.895173208 -0.802490219
 [626]  0.471295693 -0.230103424  2.236566605  0.898371040  0.684243430
 [631] -1.078537717  0.425456005 -0.913597445  0.269668990 -0.050513132
 [636] -2.866740469 -0.569515379 -0.075398224 -0.347915352  0.980992657
 [641]  1.161374481 -1.378216599  0.106279449  1.649293329  0.359421980
 [646] -1.403955743 -0.251120131  0.383054541 -0.805459300 -0.460873628
 [651]  0.530677080  0.433493888  0.585897415 -0.581625923  0.007434079
 [656] -0.165659198 -1.352611254 -0.119600862  1.608789728  1.014602163
 [661] -2.180611724 -0.295280981 -0.224985473  1.153789562 -1.137725972
 [666]  0.393362951 -0.312394219 -0.449829286  1.533588173 -0.982565503
 [671]  1.206566971  0.377880948 -0.367787267  0.139714606  0.335742909
 [676] -0.167008006  0.380507296 -1.828521424  1.037890268 -0.465699990
 [681]  0.823450451  0.100144868  0.542848095  0.742208514  0.910867271
 [686]  0.147645168  0.221629687  1.187072315 -1.213556572  0.852636931
 [691]  0.732617608 -0.501176942  1.506346009  0.851484162  0.236426447
 [696] -0.584802136 -0.363108022  0.586074764 -1.245150625 -0.338141957
 [701]  2.015580026  0.929922214 -0.799097206  0.163742795 -2.217899075
 [706]  1.168049792  1.371471011 -1.229876949  0.374513774  0.776904759
 [711]  0.442382935  0.657825567  2.446193256  1.447906349  1.531410480
 [716] -1.906739281  0.062889432 -2.074484436  0.452062108  1.697586072
 [721] -1.198012693  1.113338588  1.410311162 -0.790544182  0.158565840
 [726]  0.254325397  0.353372096 -0.390253890  0.660939583 -0.871763079
 [731] -1.244130503 -1.307864384  0.457843616  0.562438974  0.968218113
 [736] -2.302812776 -0.660462958 -0.760966327  1.080092006 -0.041235802
 [741]  1.446200413  1.106362527  0.658845814  0.778357966 -0.906162120
 [746] -0.441570460 -0.073164947  0.958574920  0.779017578  0.621102691
 [751]  1.074554538 -0.560782158 -1.236215060  0.753851772  0.617895301
 [756]  1.617066797 -1.735082453  1.370157926 -0.640753753  0.075411669
 [761] -0.081005875 -0.345218643  0.514050290 -1.600095417  0.696680568
 [766] -0.406991170  0.693882518  0.175798687  0.039542472  0.292841448
 [771]  1.728794462  0.159423864  0.587266031  1.589953430 -0.323264165
 [776]  1.485897738  0.471817419 -0.760316536 -0.427276028  1.167560630
 [781] -2.115967242  0.693147945 -0.312823924 -0.479927071  2.869214369
 [786] -0.103764754  0.832385817 -0.244370315  1.277702270  0.471163288
 [791] -1.065009332  0.367630580  0.375646494  0.728116343  0.746479429
 [796] -0.728978858  0.549894919 -1.330713632 -1.094666612  0.175947527
 [801] -1.196869499  0.399868576 -0.669361592 -1.287472421  1.843050088
 [806]  0.101553558 -0.560857270 -0.526696076 -1.676184167  1.208291257
 [811]  0.302698483 -0.494572094  0.415829081  0.103439618  0.218805250
 [816] -1.063487623  0.067818916 -2.165242209 -1.119450855 -0.140979816
 [821] -0.617082788  1.125549365  0.554456990 -0.824441042  0.472524031
 [826]  0.430356435  0.956337910 -0.471342458  0.642147610  0.317599581
 [831] -0.609961174  0.358878826  0.257075588 -0.292532618  1.262957003
 [836] -1.142523196  0.041312717  0.001664319 -0.085018941  0.089754869
 [841] -0.913411541 -0.847099694 -1.029739129  1.382055238  0.217566081
 [846] -0.609830157  0.257456470 -0.008577711 -0.161969579  0.506578511
 [851]  0.796788550  0.481098008  1.093902281  0.872914846  0.627780558
 [856]  0.384847438 -0.191057896  1.184833779  0.064899856  0.505549660
 [861]  0.238159406  1.393983385 -0.096757461  0.062795437  0.890398279
 [866]  0.731005613 -0.071453599  1.053172245 -0.160762071  0.340386058
 [871] -0.746597803 -0.432866052 -2.214414195  1.649963034  2.062067409
 [876] -1.013817801  0.323441816 -0.599596084  1.681977108  1.413137970
 [881]  0.087604201  1.010408500 -1.057306740  0.084706351  1.541831048
 [886]  1.115848612  0.323782365 -0.164080426 -0.586158285  0.493925264
 [891] -1.653506630 -0.034997490 -0.757722792 -0.391616904  3.160271061
 [896] -0.868613961 -0.089899224  1.447959591 -1.031791136  0.615010907
 [901]  0.957300539  1.395176166 -1.059221943  1.120808754 -0.776713518
 [906]  0.373513977 -0.249844275  1.327454254 -0.800754260  0.502199894
 [911]  0.194512173 -0.195176660 -0.398270845  1.109692751  1.539622484
 [916]  0.578487181 -1.531167659 -0.701583207 -0.006972894 -0.345612635
 [921] -0.129838911  1.076078700 -0.516891792 -0.703381108 -1.056561708
 [926]  0.841801277 -1.042177916 -0.080567353  0.200496732 -0.838549721
 [931] -2.785859025  0.837543464  0.787310170  0.822294251 -0.127360270
 [936]  0.647534313 -1.990128269  0.880364492 -0.306205207 -1.939921239
 [941]  0.093547178  1.378642798 -0.381748918 -0.541055117 -0.129012714
 [946] -0.069575070 -0.239731684 -0.211841134 -1.093325293  1.684012222
 [951]  0.986358506  2.186655721 -0.460792937 -1.056228612  0.453992304
 [956] -0.062342708 -1.983132942  1.048270342  1.233380926 -1.120602189
 [961] -0.714491035 -1.121018245 -0.868056056 -1.110572423  0.283992653
 [966] -0.412593173  0.086424983 -1.362957972 -0.118158779 -0.037461741
 [971] -1.204959921 -0.958445344 -1.216016069  1.217527560 -0.574355396
 [976]  0.639537004  0.800504371  0.634663806  1.699020450 -0.493150732
 [981] -0.852791214  2.063361199 -1.888678599  1.883053339  0.846120698
 [986] -0.949709308 -0.004963514  1.169338444  1.344965012  1.153031451
 [991]  1.194560986 -0.019553016 -1.367008894  0.459659431 -0.522504367
 [996] -0.020307317 -0.821358099 -2.318728426 -0.834625208 -0.947701229

Random assignment using the Binomial Distribution

Remember, we then randomly assigned them to one of two groups: A or B.

  • I used random draws from the Binomial (read: binary or two) distribution to do this.

Random assignment using the Binomial Distribution

rbinom(n = 1000, size = 1, prob = 0.5)
   [1] 1 1 1 1 0 0 1 0 0 0 0 1 1 0 0 1 1 1 0 0 0 1 0 0 1 1 1 0 1 0 0 0 0 1 1 1 0
  [38] 0 0 1 0 0 1 1 1 1 0 1 0 1 1 1 0 0 0 0 1 1 1 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0
  [75] 0 0 1 1 1 0 1 1 1 1 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 1 0 1 1 1 1 1 1 1 1 0 1
 [112] 1 0 1 0 1 1 1 0 1 1 1 1 0 0 1 0 0 1 0 1 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 1 1
 [149] 0 0 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 0 0
 [186] 1 0 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 1 1 1 0 1 0 0 1 1
 [223] 0 1 1 0 1 1 1 0 0 0 1 0 1 0 1 0 0 1 1 1 0 0 0 1 1 0 0 1 1 1 1 1 1 0 0 1 0
 [260] 1 0 1 0 1 0 0 0 0 1 0 0 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1
 [297] 1 0 1 1 1 0 0 1 1 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 0 1 0 0 1 0 0 0 0 0 1 1 0
 [334] 0 0 1 1 1 0 1 1 0 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1 0 1 1 1 1 0 0 1 0 0 0 0 0
 [371] 0 0 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 1 0 0 0
 [408] 1 0 0 0 1 1 0 0 0 0 0 1 1 0 0 1 1 0 1 1 1 0 1 1 1 1 0 0 1 1 0 1 0 1 1 1 1
 [445] 0 1 1 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 1 0 1 1 0 1 0 0 0 1 1 0 0 0 1
 [482] 1 0 0 1 0 1 1 1 1 0 0 1 0 0 0 1 0 0 1 0 1 1 1 0 1 1 0 1 0 1 0 1 0 0 1 1 1
 [519] 0 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 1 0 0 1 1 0 0 1 0 0 0 1 1 0 0 1 0 0 1 0 1
 [556] 0 0 0 1 0 0 1 0 0 0 1 1 1 1 1 0 1 0 1 1 1 1 0 1 0 0 0 0 0 0 1 0 1 1 1 1 0
 [593] 1 0 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 0 1 1 0 1 0 0 1 1 1 1 0 1 1
 [630] 1 1 1 0 1 1 0 0 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 1 1 0 0 0 0 1 0 0 1 0 0 1
 [667] 0 1 0 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 1 1 0 0 1 0 1 0 0 1 1 0 0 0 0 1
 [704] 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 0 0 0 1 0 0 1 1 1 1 1 0 0 1 0 1 1 0 0 1 0 0
 [741] 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 1 1 0 0 0 0 0 1 1 0 0 1 0
 [778] 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 1 1 1 1 0 1 0 1 1 1 0 0 0 1 1 0 0 1 0 1 1 0
 [815] 0 0 1 0 1 0 1 1 1 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 0 0 1 1 1 0 1 0 1 0 0 0 1
 [852] 1 0 1 0 1 1 0 1 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0 1 1 1 0
 [889] 1 1 0 1 1 1 1 1 0 0 1 1 0 0 0 1 1 1 1 1 0 1 1 0 1 1 1 1 0 1 1 0 1 1 0 0 0
 [926] 0 0 0 1 1 1 0 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 0 1 1
 [963] 1 1 1 0 1 0 1 0 0 1 0 0 0 0 0 1 1 0 1 1 1 0 0 0 0 1 0 0 0 1 1 0 1 1 0 1 0
[1000] 1

The Binomial Distribution

ggplot() + 
  geom_bar(aes(x = rbinom(n = 1e6, size = 1, prob = 0.5))) + 
  theme_minimal()

Assigning our people with mutate()

assigned_group <- group_df |> 
  mutate(
    group = rbinom(1000, 1, 0.5),
    group = factor(group, labels = c("A", "B"))
  )

assigned_group
# A tibble: 1,000 × 5
      id height weight eye_colour group
   <int>  <dbl>  <dbl> <chr>      <fct>
 1     1   167.   87.7 Grey       B    
 2     2   174.   88.9 Brown      A    
 3     3   166.   67.3 Blue       B    
 4     4   167.   75.0 Blue       A    
 5     5   171.   79.3 Green      A    
 6     6   171.   93.4 Blue       A    
 7     7   169.   73.0 Blue       A    
 8     8   171.   97.0 Brown      A    
 9     9   168.  101.  Grey       B    
10    10   177.   63.7 Green      B    
# ℹ 990 more rows

Comparing our two groups

Comparing our two groups

Comparing our two groups